Compact effective potentials, which replace the atomic core electrons in molecular calculations, are presented for atoms in the first and second rows of the periodic table. The angular-dependent components of these potentials are represented by compact one- and two-term Gaussian expansions obtained directly from the appropriate eigenvalue equation. Energy-optimized Gaussian basis set expansions of the atomic pseudo-orbitals, which have a common set of exponents (shared exponents) for the s and p orbitals, are also presented. The potentials and basis sets have been used to calculate the equilibrium structures and spectroscopic properties of several molecules. The results compare extremely favorably with corresponding all-electron calculations.